Tukey's One Degree of Freedom for Non-Additivity

OmegaTiger493 — Fri, 09 Jun 2023 01:01:27 GMT

Dear Community,

I am a professor and I am (slowly) incorporating new JMP Pro content into my chemistry courses. One topic I cover is Tukey's 1 degree of freedom test for nonadditivity when you have non-replicated factorials. Are there any alternatives to run this test with JMP Pro (I haven't found anything online).

thanks

Rita

Re: Tukey's One Degree of Freedom for Non-Additivity

Dan_Obermiller — Thu, 27 Apr 2023 15:55:10 GMT

I don't think there is any built-in way to get this test, but you can use some JSL to build it. The steps are: Fit your 2-way ANOVA model. Save the predicted values. Square them. Now fit the 2-way model again, but adding the squared values as a column. That test is your non-additive test. I have included a sample dataset with a script that does this. Here is the script that I used that is hard-coded for this example.

Names Default to Here(1);

dt = Current Data Table();
// Launch platform: Fit Least Squares
dt = Current Data Table();
Mod1 = dt << Fit Model(
	Y( :Impurity ),
	Effects( :Temp, :Pressure ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(
		:Impurity << {Summary of Fit( 1 ), Analysis of Variance( 1 ),
		Parameter Estimates( 1 ), Lack of Fit( 0 ), Scaled Estimates( 0 ),
		Plot Actual by Predicted( 1 ), Plot Regression( 0 ),
		Plot Residual by Predicted( 1 ), Plot Studentized Residuals( 0 ),
		Plot Effect Leverage( 1 ), Plot Residual by Normal Quantiles( 0 ),
		Box Cox Y Transformation( 0 )}
	), Invisible
);
mod1 << Prediction Formula;
mod1 << Close Window();


// New formula column: Pred Formula Impurity^2
dt << New Formula Column(
	Operation( Category( "Transform" ), "Square" ),
	Columns( :Pred Formula Impurity )
);

// Change column name: Pred Formula Impurity^2 → Nonadd
dt:"Pred Formula Impurity^2"n << Set Name( "Non-Additive Test" );


// Launch platform: Fit Least Squares
dt << Fit Model(
	Y( :Impurity ),
	Effects( :Temp, :Pressure, :"Non-Additive Test"n ),
	Personality( "Standard Least Squares" ),
	Emphasis( "Effect Leverage" ),
	Run(
		:Impurity << {Summary of Fit( 0 ), Analysis of Variance( 0 ),
		Parameter Estimates( 1 ), Sequential Tests( 1 ), Lack of Fit( 0 ), Scaled Estimates( 0 ),
		Effect Tests( 0 ),
		Plot Actual by Predicted( 0 ), Plot Regression( 0 ),
		Plot Residual by Predicted( 0 ), Plot Studentized Residuals( 0 ),
		Plot Effect Leverage( 0 ), Plot Residual by Normal Quantiles( 0 ),
		Box Cox Y Transformation( 0 )}
	)
);

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Tukey's One Degree of Freedom for Non-Additivity

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